Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations. This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.

From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.

This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries. There is special emphasis on algorithmic aspects and the use of the theory of Gröbner bases.

Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two covers finite field linear algebra; Part Three covers the solution of Polynomial Systems of Equations, with a survey of the methods used in practice, including SAT-solvers and the methods of Nicolas Courtois. Topics include: Analytic Combinatorics, and its application to cryptanalysis The equicomplexity of linear algebra operations Graph coloring Factoring integers via the quadratic sieve, with its applications to the cryptanalysis of RSA Algebraic Cryptanalysis is designed for advanced-level students in computer science and mathematics as a secondary text or reference book for self-guided study. This book is suitable for researchers in Applied Abstract Algebra or Algebraic Geometry who wish to find more applied topics or practitioners working for security and communications companies.

In the new era of technology and advanced communications, coding theory and cryptography play a particularly significant role with a huge amount of research being done in both areas. This book presents some of that research, authored by prominent experts in the field.The book contains articles from a variety of topics most of which are from coding theory. Such topics include codes over order domains, Groebner representation of linear codes, Griesmer codes, optical orthogonal codes, lattices and theta functions related to codes, Goppa codes and Tschirnhausen modules, s-extremal codes, automorphisms of codes, etc. There are also papers in cryptography which include articles on extremal graph theory and its applications in cryptography, fast arithmetic on hyperelliptic curves via continued fraction expansions, etc. Researchers working in coding theory and cryptography will find this book an excellent source of information on recent research.